Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes have not been classroom tested and may have typographical errors.

1. Fundamentals of Measure and Integration Theory.

• 1.4. Lebesgue-Stieltjes Measure and Distribution Functions (Partial). Section 1.4 notes
• Supplement. Examples, Exercises, and Proofs from Section 1.4. Beamer file of Section 1.4 examples and proofs
• Supplement. Printout of Examples, Exercises, and Proofs from Section 1.4. Print file of Section 1.4 examples and proofs
• Study Guide 1.

4. Basic Concepts of Probability.

• 4.1. Introduction. Section 4.1 notes
• 4.2. Discrete Probability Spaces. Section 4.2 notes
• 4.3. Independence. Section 4.3 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.3. Beamer file of Section 4.3 examples and proofs
• Supplement. Printout of Examples, Exercises, and Proofs from Section 4.3. Print file of Section 4.3 examples and proofs
• 4.4. Bernoulli Trials. Section 4.4 notes
• 4.5. Conditional Probability. Section 4.5 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.5. Beamer file of Section 4.5 examples and proofs
• Supplement. Printout of Examples, Exercises, and Proofs from Section 4.5. Print file of Section 4.5 examples and proofs
• 4.6. Random Variables. Section 4.6 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.6. Beamer file of Section 4.6 examples and proofs
• Supplement. Printout of Examples, Exercises, and Proofs from Section 4.6. Print file of Section 4.6 examples and proofs
• 4.7. Random Vectors.
• 4.8. Independent Random Variables (Partial). Section 4.8 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.8. Beamer file of Section 4.8 examples and proofs
• Supplement. Printout of Examples, Exercises, and Proofs from Section 4.8. Print file of Section 4.8 examples and proofs
• 4.9. Some Examples from Basic Probability.
• 4.10. Expectation.
• 4.11. Infinite Sequences of Random Variables.
• Study Guide 4.

5. Conditional Probability and Expectation.

• 5.1. Introduction.
• 5.2. Applications.
• 5.3. The General Concept of Conditional Probability and Expectation.
• 5.4. Conditional Expectation Given a σ-Field.
• 5.5. Properties of conditional Expectation.
• 5.6. Regular Conditional Probabilities.
• Study Guide 5.

6. Strong Laws of Large Numbers and Martingale Theory.

• 6.1. Introduction.
• 6.2. Convergence Theorems.
• 6.3. Martingales.
• 6.4. Martingale Convergence Theorems.
• 6.5. Unifrom Integrability.
• 6.6. Uniform Integrability and Martingale Theory.
• 6.7. Optional Sampling Theorems.
• 6.8. Applications of Martingale Theory.
• 6.9. Applications to Markov Chains.
• Study Guide 6.

7. The Central Limit Theorem.

• 7.1. Introduction.
• 7.2. The Fundamental Weak Compactness Theorem.
• 7.3. Convergence to a Normal Distribution.
• 7.4. Stable Distributions.
• 7.5. Infinitely Divisible Distributions.
• 7.6. Uniform Convergence in the Central Limit Theorem.
• 7.7. The Skorokhod Construction and Other Convergence Theorems.
• 7.8. The k-Dimensional Central Limit Theorem.
• Study Guide 7.

8. Ergodic Theory.

• 8.1. Introduction.
• 8.2. Ergodicity and Mixing.
• 8.3. The Pointwise Ergodic Theorem.
• 8.4. Applications to Markov Chains.
• 8.5. The Shannon-McMillan Theorem.
• 8.6. Entropy of a Transformation.
• 8.7. Bernoulli Shifts.
• Study Guide 8.

9. Brownian Motion and Stochastic Integrals.

• 9.1. Stochastic Processes.
• 9.2. Brownian Motion.
• 9.3. Nowhere Differentiability and Quadratic Variation of Paths.
• 9.4. Law of the Iterated Logarithm.
• 9.5. The Markov Property.
• 9.6. Martingales.
• 9.7. Ito Integrals.
• 9.8. Ito's Differentiation Formula.
• Study Guide 9.

Additional chapters are:

• 1. Fundamentals of Measure and Integration Theory.
• 2. Further Results in Measure and Integration Theory.
• 3. Introduction to Functional Analysis.
• Appendices.

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